Distance

In number theory, a prime is a positive integer greater than 1 that has no positive divisors other than 1 and itself. The distance between two positive integers x and y, denoted by d(x, y), is defined as the minimum number of multiplications by a prime or divisions (without a remainder) by a prime one can perform to transform x into y. For example, d(15, 50) = 3, because 50 = 15 * 2 * 5 / 3, and you have to perform two multiplications (*2, *5) and one division (/3) to transform 15 into 50.

For a set S of positive integers, which is initially empty, you are asked to implement the following types of operations on S.

1.  I x: Insert x into S. If x is already in S, just ignore this operation.
2.  D x: Delete x from S. If x is not in S, just ignore this operation.
3.  Q x: Find out a minimum z such that there exists a y in S and d(x, y) = z.

The input contains multiple test cases. The first line of each case contains an integer Q (1 <= Q <= 50000), indicating the number of operations. The following lines each contain a letter ‘I’, ‘D’ or ‘Q’, and an integer x (1 <= x <= 1000000).
Q = 0 indicates the end of the input.
The total number of operations does not exceed 300000.

For each case, output “Case #X:” first, where X is the case number, starting from 1. Then for each ‘Q’ operation, output the result in a line; if S is empty when a ‘Q’ operation is to perform, output -1 instead.